Markus receives dollar bills from his grandfather for one week. On the first day he received $1; on the second day he received $2, on the third day he received $4, and on the fourth day he received $8. If this continues, how much money will Markus have in total by the end of the week?

(Don't forget your units.)

Answer:

El ángulo entre el piso y la escalera está cambiando a una razón de -1 radian por segundo.

Step-by-step explanation:

Sea [tex]x[/tex] la distancia horizontal entre la pared y la base de la escalera y [tex]l[/tex] la longitud de la escalera, medidas en metros. Además, tenemos que [tex]\theta[/tex] es el ángulo entre la escalera y el piso, medido en radianes.

Si la pared y el piso son ortogonales entre sí, entonces podemos utilizar la siguiente relación trigonométrica que relaciona las variables anteriores:

[tex]\cos \theta = \frac{x}{l}[/tex]  (1)

Por diferenciación implícita y la definición de razón de cambio tenemos que:

[tex]-\sin \theta \,\dot \theta = \frac{\dot x}{l}[/tex] (2)

Donde:

[tex]\dot x[/tex] - Razón de cambio de la distancia horizontal entre la pared y la base de la escalera, medida en metros por segundo.

[tex]\dot \theta[/tex] - Razón de cambio del ángulo entre el piso y la escalera, medida en radianes por segundo.

Pero tenemos que el seno del ángulo está definido por:

[tex]\sin \theta = \frac{\sqrt{l^{2}-x^{2}}}{l}[/tex] (3)

Si aplicamos (3) en (2), expandimos la ecuación como sigue:

[tex]-\frac{\sqrt{l^{2}-x^{2}}}{l}\,\dot \theta = \frac{\dot x}{l}[/tex]

[tex]\dot \theta = - \frac{\dot x}{\sqrt{l^{2}-x^{2}}}[/tex] (4)

Si tenemos que [tex]\dot x = 5\,\frac{m}{s}[/tex], [tex]l = 13\,m[/tex] y [tex]x = 12\,m[/tex], entonces la razón de cambio del ángulo es:

[tex]\dot \theta = -\frac{\left(5\,\frac{m}{s} \right)}{\sqrt{(13\,m)^{2}-(12\,m)^{2}}}[/tex]

[tex]\dot \theta \approx -1\,\frac{rad}{s}[/tex]

El ángulo entre el piso y la escalera está cambiando a una razón de -1 radian por segundo.

The numbers are 15 and 9 .

Numbers are the basic foundation of mathematics. Numbers are used to represent quantity and used is basic arithmetic operations. Numbers can be categorized into a lot of different types such as real  or imaginary. Real numbers can be divided into integers , irrational numbers , whole numbers .The four basic arithmetic operations are multiplication , sum , division and subtraction.

Let us consider one of the given numbers be x .

Given the sum of the numbers is 21

therefore the other number = 21 - x

Now it is given that  [tex]\frac{3}{4}[/tex] of 1 number and [tex]\frac{2}{3}[/tex] of another number adds up to 15 .

∴ [tex]\frac{3}{4}[/tex] of x =  [tex]\frac{3}{4}x[/tex]  and  [tex]\frac{2}{3}[/tex] of another number =  [tex]\frac{2}{3}\times(21-x)[/tex]

Now the sum of the two new numbers is given as 15.

∴ [tex]\frac{2}{3}\times(21-x) +\frac{3}{4}x =15[/tex]

[tex]or, 14-\frac{2}{3}x +\frac{3}{4}x =15\\\\or, -\frac{2}{3}x +\frac{3}{4}x =15-14\\\\or, \frac{-8+9}{12} x=1\\\\or, \frac{1}{12}x = 1\\\\or, x=12[/tex]

So the other number is 21-12 = 9 .

Hence the two numbers are 15 and 9 .

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Answer:

5:1

Step-by-step explanation:

The ratio 10: 2 will be equivalent to ratios 20:4, 30:6, 40:8, and 50:10. Then all the options are correct.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

The equivalent is the expression that is in different forms but is equal to the same value.

The ratio is given below.

Ratio = 10 / 2

Multiply and divide the ratio by 2. Then we have

Ratio = 10 x 2 / 2 x 2

Ratio = 20 / 4

Multiply and divide the ratio by 3. Then we have

Ratio = 10 x 3 / 2 x 3

Ratio = 30 / 6

Multiply and divide the ratio by 4. Then we have

Ratio = 10 x 4 / 2 x 4

Ratio = 40 / 8

Multiply and divide the ratio by 5. Then we have

Ratio = 10 x 5 / 2 x 5

Ratio = 50 / 10

The ratio 10: 2 will be equivalent to ratios 20:4, 30:6, 40:8, and 50:10. Then all the options are correct.

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The missing options are given below.

20:4

30:6

40:8

50:10

Answer:

3n - 7 = 2n + 5

Step-by-step explanation:

n=12

that is the answer

Answer:

Equation of y in terms of x is: [tex]y = \frac{7}{4}x[/tex]

Step-by-step explanation:

Proportion means that the change in one quantity causes change in other quantity.

Given that A proportional relationship exists between x and y.

It can be expressed mathematically as:

y ∝ x

When the proportionality symbol is removed, constant of proportionality is introduced which is usually denoted as k

[tex]y = kx[/tex]

Given that y=14 when x=8

Putting in equation

[tex]14 = k * 8\\k =\frac{14}{8}\\k = \frac{7}{4}[/tex]

Putting the value of k in equation

[tex]y = \frac{7}{4}x[/tex]

Hence,

Equation of y in terms of x is: [tex]y = \frac{7}{4}x[/tex]

Transformations are used to change the position of a function from one point to another. When f(x) is reflected over the y-axis, the new function g is [tex]g(x) = x + 8[/tex]

Given that:

[tex]f(x) = -3+|x - 11|[/tex]

To reflect across the y-axis, we use the following transformation rule:

[tex](x,y) \to (-x,y)[/tex]

So, the new function is:

[tex]g(x) = f(-x)[/tex]

If [tex]f(x) = -3+|x - 11|[/tex], then:

[tex]f(-x) = -3+|-x - 11|[/tex]

Factor out -1

[tex]f(-x) = -3+|-1(x + 11)|[/tex]

Remove absolute sign

[tex]f(-x) = -3+1 \times (x + 11)[/tex]

[tex]f(-x) = -3+x + 11[/tex]

Collect like terms

[tex]f(-x) = x + 11-3[/tex]

[tex]f(-x) = x + 8[/tex]

Hence, the new function is:

[tex]g(x) = x + 8[/tex]

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Answer:

6 divided by 2 =p (a made a little graph at the bottom to demonstrate)

Step-by-step explanation:

.  .  .  .  .  .          Graph←

.  .  .  .  .  .

Answer:

if the points are in a straight line going upward then they are corect

but if the points are scattered they are wrong its hard to answer this question he graph to look at

Answer:

[tex]\%Increase = 4\%[/tex]

Step-by-step explanation:

Given

[tex]Initial\ Population = 625[/tex]

[tex]Final\ Population = 650[/tex]

Required

Determine the percentage population increase

This is calculated using the following formula:

[tex]\%Increase = \frac{Final - Initial}{Initial} * 100\%[/tex]

[tex]\%Increase = \frac{650 - 625}{625} * 100\%[/tex]

[tex]\%Increase = \frac{25}{625} * 100\%[/tex]

[tex]\%Increase = \frac{25* 100\%}{625}[/tex]

[tex]\%Increase = \frac{2500\%}{625}[/tex]

[tex]\%Increase = 4\%[/tex]

Hence, there is a 4% increment from 2014 to 2015

Answer:

280 miles

Step-by-step explanation:

So, 420 miles=12 gallons

That means that for 1 gallon you would be able to go 35 miles.

Just multiply that by 8. 35*8=280

Answer:

Option 1: -2

Step-by-step explanation:

Take the rise over the run, where rise is the number of units vertically up the graph and run is the number of units horizontally across the graph

This is a topic on coordinate geometry. If you wish to explore more into this topic you can give me a follow on Instagram (learntionary). I'll be uploading notes on this topic soon. At the meantime, you can take a look at other topics or some tips as well!

Answer:

y = 3/5x + 3/5.

Step-by-step explanation:

the /'s are division symbols.              3            3

                                                  y =     _   +       _

                                                           5            5

Answer:

A rectangular visual model resembling a piece of tape with divisions used to assist mathematical calculations. Also known as a divided bar model, fraction strip, length model or strip diagram. In mathematics education, it is used to solve word problems.

Step-by-step explanation:

Answer:

Tape diagrams are visual models that use rectangles to represent the parts of a ratio.

Here's what it looks like

Answer:

8.5

Step-by-step explanation:

8.5 is the coefficient in front of x

Answer:

12

Step-by-step explanation:

For ΔDEF similar to ΔRST, the value of x is 12. So, option a) is correct.

Two triangles are said to be similar if corresponding angles are equal or  corresponding sides are in the same proportion.

Given triangles are similar:

ΔDEF ~ ΔRST

Therefore, using the property of similar triangle that corresponding sides of a similar triangle are in same proportion.

[tex]\dfrac{EF}{ST}=\dfrac{ED}{SR}\\\\\dfrac{x}{16}=\dfrac{3}{4}\\\\x=\dfrac{3}{4}\times 16\\\\x=12[/tex]

Thus, the value of x is 12. So, option a) is correct.

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Answer:

1 mile every 6 minutes because 30 divided by 5 is 6 and 5 divided by 5 is 1

Step-by-step explanation:

I hoped this helped and if it did I would appreciate it if you marked me brainliest. Thank you and have a nice day!

Answer:

1 months

Step-by-step explanation:

Given

Anaconda

[tex]Length = 5.23m[/tex]

[tex]Growth = 1.27m[/tex] monthly

Python:

[tex]Length = 4.76m[/tex]

[tex]Growth = 2.04m[/tex] monthly

Required

Determine when their length will be equal

First, we need to write equations that determines the growth of each snake in m months.

For both snakes;

[tex]Expression = Length + Growth * m[/tex]

For the Anaconda, the expression is:

[tex]5.23 + 1.27 * m[/tex]

[tex]5.23 + 1.27 m[/tex] --- (1)

For the Python, the expression is

[tex]4.76 + 2.04 * m[/tex]

[tex]4.76 + 2.04m[/tex] ---- (2)

Both snakes will have equal length when both expressions (1 & 2) are equal

[tex]4.76 + 2.04m = 5.23 + 1.27 m[/tex]

Collect Like Terms

[tex]2.04m - 1.27 m= 5.23 - 4.76[/tex]

[tex]0.77 m= 0.47[/tex]

Solve for m

[tex]m = \frac{0.47}{0.77}[/tex]

[tex]m = 0.61[/tex]

[tex]m = 1[/tex] --- Approximated

Hence, the zookeeper will wait for 1 month

Answer:

The slope is 6 and the y intercept is -5

Step-by-step explanation:

y=6x-5

The equation is in slope intercept form

y = mx+b where m is the slope and b is the y intercept

The slope is 6 and the y intercept is -5

Answer:

[tex]slope=6\\\\y-intercept=-5[/tex]

Step-by-step explanation:

The given equation is written in slope-intercept form:

[tex]y=mx+b[/tex]

where:

Find the values:

[tex]y=(slope)x+(y-intercept)\\\\y=6x-5[/tex]

6 is in the slope place, so the slope is 6.

5 is in the y-intercept place. Note how this number has a negative sign when the original equation says "+b". This means that the y-intercept is -5.

:Done

Answer:

B- y=-3

Step-by-step explanation:

Answer:

I got x = -3/7, y = 20/7. Hope this helps :)

Answer:

12.6 cups

Step-by-step explanation:

each liter has 4.2 cups so if you just multiply it by 3 you will get 12.6. cups.

Answer:

Length=3x^3+6x^2+10x+10

Step-by-step explanation:

given that the area A of a rectangle is A=L*W, we can find length L=A/W

Answer:

X=$7

Step-by-step explanation:

Answer:

x=19

Step-by-step explanation:

subtract 12 from each side: 50-12=2x+12-12

38=2x

divide by 2

38/2=2x/2

19=x

Answer:

x=19

Step-by-step explanation:

50=2x+12

50-12=2x+12-12

38=2x

38/2=2x/2

x=19

Answer:

55

Step-by-step explanation:

6(10)-5

=60-5

=55

PLS GIVE BRAINLIEST

Answer:

55

Step-by-step explanation:

for this problem, you would use substitution. What you do is replace the x in the 6x-5 expression with 10 (since x is already solved for 10).

6x-5 and x=10

substitute x for 10

6(10)-5

simplify

60-5

answer

55

Answer:

0.749

Step-by-step explanation:

We start by calculating the z-score

Mathematically:

z-score = (x-mean)/SD

z-score = (75-77)/3 = -2/3 = -0.67

The probability we want to calculate is;

P( X > -0.67)

we can use the standard normal distribution table for this

Using this table, the probability has a value 0.74857 which is 0.749 to the nearest thousandth